How can I remove multiple overlapping vertices?
I'm not sure I understand your question, but I believe you are asking how to remove overlapping vertices, or how to get rid of obscured vertices under a face. 

For the first case: Press A to select everything in the scene. Then press w. A menu will pop up, and one option will be "Remove doubles." "Remove doubles" gets rid of all overlapping vertices.

For the second case, I would go into wireframe mode(press "z") and check if I could get rid of the problem manually by selecting and deleting the vertices. If that does work, I'd select around the problemed area using circle select(press "c"), and then bring up the delete menu(press "x") and select "limited dissolve." On the left-hand side in the toolbar tab, there will be a section that says "normals" with an adjustment bar. Fidget with the adjustment bar to see if any condition works.